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It is suggested to derive formulae (dependences on symbolic parameters) by means of restoration upon a set of fixed exact numeric values of the parameters. The main tool is Pade interpolation. The problem of distortion of structure of restored expressions and, to some extent, the problem of verification of results are considered. A statistical treatment of… (More)

The perturbed motion in the neighborhood of regular precession of a dynamically symmetric satellite on a circular orbit is studied. The " Norma " specialized program package [1,2], intended for normal-ization of autonomous Hamiltonian systems by means of computer algebra, is used to obtain normal forms of the Hamiltonian. A full catalogue of non-resonant… (More)

Algorithms of numeric (in exact arithmetic) deduction of analytical expressions, proposed and described by Shevchenko and Vasiliev (1993), are developed and implemented in a computer algebra code. This code is built as a superstructure for the computer algebra package by Shevchenko and Sokolsky (1993a) for normalization of Hamil-tonian systems of ordinary… (More)

Notwithstanding a three-centennial progress in studies of the three-body problem, disruption of a three-body gravitational system still remains an enigmatic dynamical process. We consider statistics of the disruption and Lyapunov times in a general hierarchical three-body problem. We show that at the edge of disruption the orbital periods of the escaping… (More)

- I. I. Shevchenko
- 2008

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. An especially designed software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is used to obtain normal forms of the Hamiltonian in the given problem. The normalization is… (More)

- I. I. Shevchenko
- 2002

The possibility of dynamic chaos in the spin motion of minor natural planetary satellites is studied numerically and analytically. A satellite is modelled as a tri-axial rigid body in a fixed elliptic orbit. The Lyapunov characteristic exponents (LCEs) are used as indicators of the degree of chaos of the motion. For a set of real satellites (i.e. satellites… (More)

- V. V. Kouprianov, I. I. Shevchenko

The chaotic behavior in the rotational motion of planetary satellites is studied. A satellite is modelled as a triaxial rigid body. For a set of twelve real satellites, as well as for sets of model satellites, the full spectra of the Lyapunov characteristic exponents (LCEs) of the chaotic spatial rotation are computed numerically. The applicability of the "… (More)

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